1 Compton telescopes for $\gamma$-ray astrophysics

Looking beyond the INTErnational Gamma-Ray Astrophysics Laboratory (INTEGRAL), the next generation soft $\gamma$-ray ( $\sim 0.2-20$ MeV) observatory will require high angular and spectral resolution imaging to significantly improve sensitivity to astrophysical sources of nuclear line emission. Building upon the success of COMPTEL/CGRO (Schönfelder et al. 1993), and the high spectral resolution of the upcoming SPI/INTEGRAL (Vedrenne et al. 1998; Lichti et al. 1996), a number of researchers (Johnson et al. 1995; Jean et al. 1996; Boggs 1998) have discussed the merits of a high spectral/angular resolution germanium Compton telescope (GCT); the ability to achieve high sensitivity to point sources while maintaining a large field-of-view make a high resolution Compton telescope an attractive option for the next soft $\gamma$-ray observatory.

The development of Compton telescopes began in the 1970's, with work done at the Max Planck Institut (Schönfelder et al. 1973), University of California, Riverside (Herzo et al. 1975), and the University of New Hampshire (Lockwood et al. 1979), culminating in the design and flight of COMPTEL/CGRO. These historical Compton telescopes consist of two scintillation detector planes - a low atomic number "converter'' and a high atomic number "absorber''. The model interaction of a Compton telescope is a single Compton scatter in the converter plane, followed by photoelectric absorption of the scattered photon in the absorber. By measuring the position and energy of the interactions, the event can be reconstructed to determine the initial photon direction to within an annulus on the sky.

A handful of groups are actively developing imaging germanium detectors (GeDs) partly in anticipation of a GCT (Luke et al. 1994; Kroeger et al. 1995). The goal of these researchers is to develop large area detectors with (sub)millimeter spatial resolution, while maintaining the high spectral resolution ( $E/\delta E \sim 500$ at 1 MeV) characteristic of GeDs. The use of high spectral/spatial resolution GeDs as converter and absorber planes would significantly improve the performance of a Compton telescope, but will add a number of complications to the event reconstruction. Most significantly, with the moderate atomic number (Z = 32) of germanium, photons will predominantly undergo multiple Compton scatters before being photoabsorbed in the instrument. Furthermore, with interaction timing capabilities of $\sim$10 ns, the interaction order will not be determined unambiguously by timing alone. Compton Kinematic Discrimination (CKD) is proposed here to overcome these complications, an extension of a method first discussed in context of liquid xenon time projection chambers (Aprile et al. 1993). The ability of this technique to allow proper event reconstruction is investigated in detail.

Due to their relatively low efficiency (typically $\sim 1\%$), Compton telescopes rely on efficient background suppression to maintain their sensitivity. In addition to interaction ordering, techniques are presented using CKD, in combination with other tests and restrictions, to suppress the dominant background components.

The goal of this work is to outline a complete set of event reconstruction techniques for GCTs, taking into account realistic detector/instrument performance and uncertainties. Examples of the techniques are presented for a GCT configuration outlined in Appendix A; however, full analysis of this configuration will be presented in a second paper dedicated to the optimization and performance of several GCT configurations. The full analysis of a GCT configuration is complicated, requiring a detailed study of the tradeoffs between efficiency, angular and spectral resolution; therefore, this paper focuses only on the detailed discussion of the event reconstruction techniques which will be used in future work dedicated to analyzing GCT performance.

Figure 1: Example Compton telescope. If a photon undergoes one or more Compton scatters in the instrument and then is photoelectrically absorbed, then by using the positions $(\vec{r}_{1}, \ldots,\vec{r}_{N})$ and energy deposits $(E_{1}, \ldots, E_{N})$ of the interactions, the initial direction of the photon can be determined by the Compton scatter formula to within an annulus on the sky, $\phi _{1}$. The width of this annulus is determined by the uncertainties in both the interaction locations and energy deposits